$10C_{2}F=20C_{3}F\text{ and }20C_{3}F=40F$

$\left\{\begin{matrix}\\F=0\text{, }&\text{unconditionally}\\F\in \mathrm{R}\text{, }&C_{2}=4\text{ and }C_{3}=2\end{matrix}\right.$

$\left\{\begin{matrix}C_{3}=2\text{, }&C_{2}=4\\C_{3}\in \mathrm{R}\text{, }&F=0\end{matrix}\right.$